Critical flow based mass flow verifier

ABSTRACT

A flow verifier for verifying measurement by a fluid delivery device under test (DUT) includes a chamber configured to receive a flow of the fluid from the DUT, at least one temperature sensor to provide gas temperature in the chamber, at least one pressure transducer to provide gas pressure in the chamber, and a critical flow nozzle located upstream of the chamber along a flow path of the fluid from the DUT to the chamber. The critical flow nozzle and the flow verification process are configured to maintain the flow rate of the fluid through the nozzle at the critical flow condition such that the flow rate through the nozzle is substantially constant and substantially insensitive to any variation in pressure within the chamber downstream of the nozzle. Therefore, the varying chamber pressure during the flow verification period has substantially no impact on the downstream pressure of the DUT, and the external volume between the flow verifier and the DUT is substantially irrelevant to the flow verification calculation.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation-in-part application of: U.S. patentapplication Ser. No. 11/090,120 (the “'120 application”) filed on Mar.25, 2005, now U.S. Pat. No. 7,174,263, entitled “External VolumeInsensitive Flow Verification.” The contents of this application isincorporated herein by reference in its entirety as though fully setforth.

BACKGROUND

High-precision fluid delivery systems such as mass flow controllers(MFCs) and mass flow ratio controllers (FRCs) are very important inapplications such of semiconductor wafer fabrications. In manyinstances, the accuracy of these fluid delivery systems need to beverified.

A rate-of-rise (ROR) flow verifier may be used to verify the accuracy ofmeasurement systems such as MFCs or FRCs. A typical ROR flow verifiermay include a chamber, a pressure transducer, a temperature sensor andtwo isolation valves, one upstream and one downstream. The valves may beclosed during idle, and may open when a run is initiated, allowing flowof fluid from the device under test (DUT) such as a MFC or a FRC throughthe flow verifier. Once fluid flow has stabilized, the downstream valvemay be closed, and as a result the pressure may rise in the chamber, andthe raise in pressure may be measured as well the gas temperature. Thesemeasurements may be used to calculate the flow rate and thereby verifythe performance of the DUT.

The rising pressure in the chamber of a ROR verifier may be a majordisturbance to the verification process. Although the DUT may adjust itsvalve position to offset the downstream pressure (chamber pressure)disturbance in order to maintain the targeted flow set point, the flowfluctuation may occur and undermine the flow rate verification process.A mass flow verification system and method are needed that can avoidsuch a disturbance to the DUT.

The connecting flow path volume between the DUT and the ROR flowverifier is called the external volume. It needs to be determined inorder to calculate the flow rate by the ROR flow verifier. However, thesetup calibration process for determining external volumes is verytime-consuming if there are many DUTs connected to the ROR verifier sothat a different external volume results for each DUT. Furthermore, theaccuracy of flow verification by a ROR decreases as the external volumeincreases. This is because the pressure drop along the flow path, i.e.the pressure change (measured by the pressure transducer) in the chamberof a ROR, is different from the pressure change along the flow path. Thelonger the flow path, the lesser the accuracy of flow verification. Amass flow verification system and method are needed in order to solvethe external volume problem for the ROR verifier.

SUMMARY

An ROR verifier for verifying measurement by a fluid delivery device isdescribed. The flow verifier includes a chamber configured to receive aflow of the fluid from the device, a temperature sensor configured tomeasure the gas temperature, and a pressure sensor configured to measurepressure of the fluid within the chamber. The flow verifier includes acritical flow nozzle located at the inlet of the chamber along a flowpath of the fluid from the device under test (DUT) to the chamber. Thecritical flow nozzle is configured to maintain, during a critical flowtime period t_(cf), the flow rate of the fluid through the nozzle andthe upstream pressure of the nozzle (the downstream pressure of the DUT)substantially constant, and substantially insensitive to variation inpressure within the chamber.

A method of minimizing the disturbance to the DUT by a ROR verifierduring the verification process includes providing a critical flownozzle between the flow delivery device and the mass flow verifier so asto maintain flow of the fluid across the nozzle so that flow rate of thefluid through the nozzle is substantially insensitive to variations inpressure within the chamber as long as ratio of downstream pressure ofthe nozzle and upstream pressure of the nozzle is less than a criticalflow parameter α_(pc).

A ROR flow verification method for solving the external volume problemincludes placing a critical flow nozzle at the inlet of the chamber of aROR verifier such that the flow verification process is insensitive toexternal volumes and the information about external volumes isirrelevant to the flow verification calculation by the ROR verifier.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a block diagram of critical flow based mass flow verifier, inaccordance with one embodiment of the present disclosure.

FIG. 2 is a graph illustrating the response of the critical flow basedmass flow verifier shown in FIG. 1.

FIG. 3 illustrates a continuous pulse semi-real time operation of thecritical flow based mass flow verifier shown in FIG. 1.

FIG. 4 schematically illustrates add-on critical flow nozzles for a massflow verifier.

DETAILED DESCRIPTION

FIG. 1 is a block diagram of critical flow based mass flow verifier(MFV) 100, in accordance with one embodiment of the present disclosure.In the illustrated embodiment, the MFV 100 is a rate-of-rise (ROR) typeof MFV in which the rate of rise of pressure of fluid flowing into anenclosed chamber is measured and used to verify the flow rate into thechamber. The MFV 100 is a critical flow based MFV that includes a flowrestrictor 140, which may be a critical flow nozzle 140. While acritical flow nozzle 140 is described as a convergent nozzle for theillustrated embodiment described below, other embodiments of thisdisclosure may use other types of critical flow nozzles, such as aconvergent-divergent critical flow nozzle, and may use any deviceincluding any type of critical flow restriction such as a critical floworifice.

As described further below, the critical flow nozzle 140 maintains theflow through the nozzle 140 constant, so that the mass flow testing bythe MFV 100 is substantially insensitive to the rising pressure withinthe chamber. The critical flow nozzle 140 thus greatly minimizes thedownstream pressure disturbance to the device under test (DUT) such thatthe DUT has the minimum flow fluctuation during the flow verificationprocess. The critical flow nozzle 140 also renders the mass flowverification by the MFV 100 substantially insensitive to any externalvolume between the critical flow nozzle 140 and the DUT.

The MFV 100 includes an enclosed volume or chamber 130 that isconfigured to receive a flow of a fluid from a DUT 110. The DUT 110 istypically a mass flow controller (MFC) or a mass flow ratio controller(FRC) that delivers the flow rate of the fluid. A downstream outletvalve 150 shuts on and off the flow of the fluid from the chamber 130.An upstream inlet valve 120 shuts on and off the flow of fluid from theDUT 110 into the chamber 130. The MFV 100 further includes a pressuresensor 170 configured to measure pressure of the fluid within thechamber 130, and a temperature sensor 180 configured to measuretemperature of the fluid within the chamber 130. Typically, the fluidwhose mass flow rate is being verified is a gas, although flow rates ofother types of fluids may also be verified by the MFV 100.

The basic principle of a ROR MFV is a mass balance over the chamber 130.Using the mass balance equations, and applying the ideal gas law to thegas in the chamber, the inlet gas flow rate can be obtained by measuringthe gas pressure and the gas temperature in the chamber of MFV accordingto the following equation:

$\begin{matrix}{Q_{in} = {\frac{k_{0} \cdot T_{stp} \cdot V_{c}}{P_{stp}}\frac{\mathbb{d}}{\mathbb{d}t}( \frac{P}{T} )}} & (1)\end{matrix}$

where k₀ is a conversion constant, 6×10⁷ in SCCM (standard cubiccentimeters per minute) units and 6×10⁴ in SLM (standard liters perminute) units; P_(stp) is the standard pressure (=1 atm), Tstp is thestandard temperature (=273.15K), where P is the chamber gas pressure,V_(c) the chamber volume, and T is the gas temperature.

The MFV 100 includes a controller 160 that receives the output signalsof the pressure sensor 170 and temperature sensor 180 and controls theoperation of the upstream valve 120 and the downstream valve 150. Thecontroller 160 measures a rate of rise in pressure of the fluid withinthe chamber after the downstream valve is closed, and using the measuredrate of rise of pressure over time and temperature to calculate the flowrate of the fluid from the DUT into the chamber according to Eq. (1),thereby verifying measurement by the DUT.

A typical mass flow verification procedure is as follows:

-   -   1. Open both the upstream valve 120 and the downstream valve        150;    -   2. Give a flow set point for the DUT;    -   3. Wait until the chamber pressure is at steady state;    -   4. Start to record the chamber gas pressure and the chamber gas        temperature for flow calculation;    -   5. Shut the downstream valve 150 so that the chamber pressure        rises;    -   6. Wait for a period for flow verification;    -   7. Open the downstream valve 150;    -   8. Stop recording the chamber gas pressure and the chamber gas        temperature;    -   9. Calculate and report the verified flow based on Eq. (1).

The critical flow nozzle 140 is configured to maintain the flow of thefluid to a critical or choked flow. When a gas passes through arestriction, its density decreases and its velocity increases. There isa critical area at which the mass flux (the mass flow per unit area) isat a maximum. In this area, the velocity is sonic, and furtherdecreasing the downstream pressure will not increase the mass flow. Thisis referred to as critical flow or chocked flow.

In order for the critical flow condition to be satisfied, a criticalpressure ratio α_(pc) is defined as the ratio between the maximumallowable downstream pressure of the nozzle, P_(dmax), to the upstreampressure of the nozzle P_(u) as:

$\begin{matrix}{\alpha_{pc} = {\frac{P_{d,\max}}{P_{u}}.}} & (2)\end{matrix}$

The critical flow condition requires:

$\begin{matrix}{{\frac{P_{d}}{P_{u}} \leq \alpha_{pc}},} & (3)\end{matrix}$

where P_(d) is the downstream pressure of the nozzle. The criticalpressure ratio α_(pc) is a property of the flow restrictor, i.e. of thecritical flow nozzle 140. The critical pressure ratio is only dependenton the geometry of the critical flow nozzle, and intrinsic gasproperties. For ASME long-radius nozzles without diffuser and thicksquared-edged orifices, the critical pressure ratio α_(pc) can bederived based on the assumption of steady isentropic flow as:

$\begin{matrix}{\alpha_{pc} = ( \frac{2}{\gamma + 1} )^{\frac{\gamma}{\gamma - 1}}} & (4)\end{matrix}$

where y the ratio of specific heat of the gas defined as:

$\begin{matrix}{{\gamma = \frac{C_{p}}{C_{v}}},} & (5)\end{matrix}$

where C_(p) is the gas heat capacity at constant pressure, and C_(v) isthe gas heat capacity at constant volume.

Under the critical flow condition, the critical flow rate is given by:

$\begin{matrix}{{Q = {\frac{k_{0}T_{stp}}{P_{stp}T}C^{\prime}{{AP}_{u}( {\frac{RT}{M}\frac{2\gamma}{\gamma + 1}} )}^{1/2}( \frac{2}{\gamma + 1} )^{1/{({\gamma - 1})}}}},} & (6)\end{matrix}$

where k₀ is the conversion factor described above, T the gastemperature, P_(u) the upstream pressure, A the cross area of theorifice or the nozzle throat area, C′ the discharge coefficient, M themolecular weight of the gas, R the universal gas law constant, and C′ isthe nozzle discharge coefficient.

The discharge coefficient C′ accounts for the reduced cross-sectionalarea as the high speed gas stream continues to decrease in diameter,after it passes through the orifice. The value of C′ is between 0.7 to1.0.

The following gas function may be defined:

$\begin{matrix}{{f_{g}( {M,\gamma,T} )} = {( {\frac{RT}{M}\frac{2\gamma}{\gamma + 1}} )^{1/2}( \frac{2}{\gamma + 1} )^{1/{({y - 1})}}}} & (7)\end{matrix}$

Using this definition of a gas function, Eq.(6) can be simply writtenas:

$\begin{matrix}{Q = {\frac{k_{0}T_{stp}}{P_{stp}}C^{\prime}A\frac{f_{g}( {M,\gamma,T} )}{T}{P_{u}.}}} & (8)\end{matrix}$

As long as the critical flow condition of Eq.(3) maintains, thedownstream pressure will not influence the mass flow rate across therestriction, and the only way to increase the flow rate is to increasethe upstream pressure according to Eq. (8).

The critical flow based MFV (hereinafter referred to as the cMFV) has aflow restrictor such as a critical flow nozzle or orifice at theentrance of the chamber of a ROR verifier, as illustrated in FIG. 1. Ifboth the upstream valve 120 and the downstream valve 150 of the cMFV 100are open and the flow of the DUT is at steady state and the criticalnozzle is properly sized, the pressure ratio between the downstreampressure of the restrictor (the chamber pressure) and the upstreampressure of the restrictor is less than the critical pressure ratiolimit (α_(pc)). Therefore the flow across the flow restrictor is acritical flow and independent of the chamber pressure according to Eq.(8). At this steady state moment, the flow through the restrictor isequal to the flow delivered by the DUT and the upstream pressure of therestrictor (the downstream pressure of the DUT) is constant. When thedownstream valve 150 is shut for flow verification, the chamber pressurerises.

As long as the pressure ratio between the chamber pressure and theupstream pressure of the restrictor is less than the critical pressureratio (α_(pc)), the flow through the restrictor is still a critical flowand independent of the rising chamber pressure. Therefore, the flowthrough the restrictor is unchanged, the upstream pressure of therestrictor is unchanged, and there is no downstream pressure disturbanceto the DUT even as the chamber pressure is increasing. If the increasingchamber pressure exceeds the critical pressure ratio (α_(pc)), the flowthrough the restrictor is not a critical flow and it is dependent onboth the upstream and the downstream pressure of the restrictor. As aresult, the flow through the restrictor is not equal to the flowdelivered by the DUT, the upstream pressure of the restrictor changesand there is a downstream pressure disturbance to the DUT.

The critical flow period of cMFV is defined as the period between themoment when the downstream valve is completely shut and the moment whenthe rising chamber pressure exceeds the critical pressure ratio limit(α_(pc)). During the critical flow period, the flow through therestrictor is a constant critical flow and independent of the chamberpressure, and there is no downstream pressure disturbance to the DUT.The critical flow period can be obtained by integrating both sides ofequation (8) with the help Eq. (1) and Eq. (3), from a time t=0, to thecritical flow period t_(cf):

$\begin{matrix}{t_{cf} = {\frac{V_{c}( {a_{pc} -} }{C^{\prime}{Af}_{g}}\frac{ a_{p\; 0} )}{( {M,\gamma,T} )}}} & (9)\end{matrix}$

where (α_(p0)) is the initial pressure ratio between the chamberpressure and the upstream pressure of the restrictor at t=0 (at themoment when the inlet flow is stabilized before the downstream valve isshut).

As seen from equation (9), the critical flow period is only dependent onthe gas properties, the gas temperature, and the geometry of the cMFVincluding the critical flow nozzle. In other words, the critical flowperiod is independent of flow rate. If the verification time of a cMFVis within the critical flow period, the flow across the nozzle is aconstant critical flow and the rising chamber pressure does not disturbthe downstream pressure of the DUT. This greatly minimizes thedownstream disturbance to the DUT. The critical flow period is alsoproportional to the chamber volume V_(c). Increasing the criticalpressure ratio α_(pc), or decreasing the critical flow area A, thereforeincreases the critical flow period. For a given critical flow nozzle anda chamber volume, it is found that large molecular weight gases such asSF₆ and WF₆ have a much larger critical flow period than that of smallmolecular gases such as H_(e) and H₂. Hydrogen has the smallest criticalflow period in all semi-gases.

The flow restrictor such as a critical flow nozzle or orifice separatesthe chamber of a ROR verifier from the external plumbing to the DUT aslong as the critical flow condition of Eq. (3) holds. If the flowverification period is within the critical period, the critical flowthrough the restrictor is equal to the flow rate of the DUT. Clearly,the external volume between the critical flow nozzle and the DUT isirrelevant to the flow calculation of Eq. (1). There is no need forsetup calibration process to determine the external volume between theflow restrictor and the DUT for flow verification calculation.

FIG. 2 is a graph illustrating the critical flow period, as well theresponse of the critical flow based MFV 100. The graph 210 representsthe pressure of the fluid within the chamber, which rises when thedownstream valve is closed. The graph 220 represents the flow rate ofthe fluid. The critical flow period of cMFV is indicated in FIG. 2 withreference numeral 230. As seen in FIG. 2, during the critical flowperiod, the inlet flow through the nozzle is a critical or choked flow,the rising chamber pressure will not affect the inlet flow and theupstream pressure of the nozzle (which is also the downstream pressureof the DUT). After the critical flow period (during which the downstreampressure of the DUT is constant) lapses, the flow rate drops, and thedownstream pressure of the DUT changes.

If the chamber pressure can be kept always lower than the criticalpressure ratio limit during the flow verification, the flow through thenozzle will always be at the critical flow condition and the varyingchamber pressure will not disturb the downstream pressure of the DUT,which substantially minimizes the fluctuation of the actual flow of theDUT.

FIG. 3 illustrates a continuous pulse semi-real time (CPSR) operation ofthe critical flow based mass flow verifier shown in FIG. 1. The graph310 represents the pressure of the fluid within the chamber, which riseswhen the downstream valve is closed and drops when the downstream valveis opened. The graph 320 represents the flow rate of the fluid. The CPSRoperation has been developed for cMFV in order to continue to meet thecritical flow condition during the entire multiple-run flow verificationperiod. In the CPSR operation, the period between the downstream valveshut and open is within the critical flow period such that the risingchamber pressure never exceeds the critical pressure ratio limit. Asseen in FIG. 3, each flow verification run is within the critical flowperiod such that the flow across the nozzle is a critical flow. Hencethe varying chamber pressure has no impact on the upstream pressure ofthe nozzle, thus minimizing the downstream pressure disturbance to theDUT. As a result, the actual flow fluctuation of the DUT has beenminimized for the whole multiple-run flow verification period.

The output of the verification can be averaged among these multiple runsin which the inlet flow across the nozzle is constant or at the criticalflow condition, as guaranteed by the CPSR operation. In this way, thevariance caused by the measurement noise can be minimized. The CPSRoperation described in the previous paragraph is a simple and fast wayto achieve multiple runs for flow verification without disturbing thedownstream pressure of the DUT.

Critical flow nozzles are easy to be modeled, calculated, designed,manufactured and tested. The critical flow nozzle can be an add-on partto a ROR MFV. FIG. 4 schematically illustrates add-on critical flownozzles for a ROR MFV. Different orifice sizes of the critical flownozzle can be selected based on the flow range and the maximumdownstream pressure requirement for the DUT in order to achieveexcellent accuracy, repeatability, and external volume insensitivityproperties for mass flow verification.

In one embodiment, the MFV 100 may further include a second pressuretransducer 190 (shown for convenience in both FIGS. 1 and 4), locatedupstream of the flow nozzle, as a flow stability detector. The pressuretransducer 190 is configured to measure the upstream pressure of theflow nozzle 140. Once the upstream pressure of the nozzle is stabilized,the flow through the nozzle into the chamber is stabilized, and the cMFVcan immediately start the flow verification process. With the pressuretransducer 190, the cMFV can avoid having to wait for a fixed period oftime for flow to be stabilized before running the flow verificationprocess. The upstream pressure of the nozzle can be further used tocalculate the flow rate through the nozzle according to Eq. (6) as asecond flow verification mechanism. This second flow verificationmechanism can be used to diagnose the cMFV or as a second flowverification method to the cMFV.

In sum, a critical flow based MFV is presented in which a critical flownozzle is placed at the entrance of the chamber volume. The criticalflow nozzle can be an add-on part to a ROR MFV. As long as the ratiobetween the chamber pressure and the upstream pressure of the nozzle isless than the critical flow pressure ratio, the rising chamber pressurewill not affect the downstream pressure of the DUT and the flow rateacross the nozzle is constant. There is no need or setup configurationto determine the external volume between the DUT and the cMFV for flowverification. In this way, the performance of mass flow verifying interms of accuracy, repeatability, and external volume insensitivity issubstantially improved.

While certain embodiments have been described of systems and methodsfor, it is to be understood that the concepts implicit in theseembodiments may be used in other embodiments as well. The protection ofthis application is limited solely to the claims that now follow.

In these claims, reference to an element in the singular is not intendedto mean “one and only one” unless specifically so stated, but rather“one or more.” All structural and functional equivalents to the elementsof the various embodiments described throughout this disclosure that areknown or later come to be known to those of ordinary skill in the artare expressly incorporated herein by reference, and are intended to beencompassed by the claims. Moreover, nothing disclosed herein isintended to be dedicated to the public, regardless of whether suchdisclosure is explicitly recited in the claims. No claim element is tobe construed under the provisions of 35 U.S.C. §112, sixth paragraph,unless the element is expressly recited using the phrase “means for” or,in the case of a method claim, the element is recited using the phrase“step for.”

1. A flow verifier for verifying measurement by a fluid delivery device,the flow verifier comprising: a chamber configured to receive a flow ofthe fluid from the device; a pressure sensor configured to measurepressure of the fluid within the chamber; a temperature sensorconfigured to measure temperature of the fluid within the chamber; and acritical flow nozzle located upstream of the chamber along a flow pathof the fluid from the device to the chamber; wherein the critical flownozzle is configured to maintain, during a critical flow time periodt_(cf), flow rate of the fluid through the nozzle substantially constantand substantially insensitive to variation in pressure within thechamber; wherein the critical flow nozzle is configured to allow thefluid flowing through the nozzle to satisfy a critical flow conditionduring the critical flow time period t_(cf), and wherein the criticalflow condition is given mathematically by:${{\frac{P_{d}}{P_{u}} \leq a_{pc}} = ( \frac{2}{\gamma + 1} )^{\frac{\gamma}{\gamma - 1}}},$where P_(d) is pressure of the fluid within the chamber and downstreamof the critical flow nozzle, P_(u) is pressure of the fluid upstream ofthe critical flow nozzle, γ is given by γ=C_(p)/C_(v) and is a ratio ofspecific heats C_(p) and C_(v) of the fluid, where C_(p) is heatcapacity of the fluid at constant pressure, and C_(v) is heat capacityof the fluid at constant volume, and α_(pc) is critical pressure ratiorepresenting the maximum allowable ratio between P_(d) and P_(u) forwhich flow of the fluid across the nozzle will remain substantiallyconstant and substantially insensitive to any variation in pressurewithin the chamber.
 2. The flow verifier of claim 1, further comprisingan upstream valve configured to shut on and off flow of the fluid fromthe device into an inlet of the chamber, and a downstream valveconfigured to shut on and off flow of the fluid from an outlet of thechamber.
 3. The flow verifier of claim 2, further comprising: acontroller configured to control the downstream and upstream valves andthe pressure and temperature sensors, the controller further configuredto measure a rate of rise in pressure of the fluid within the chamberafter the downstream valve is closed, and using the measured rate ofrise to calculate the flow rate of the fluid from the device into thechamber, thereby verifying measurement by the fluid delivery device. 4.The flow verifier of claim 3, wherein the pressure sensor and thetemperature sensor are configured to make measurements within thecritical time period t_(c), so that the flow verification process issubstantially independent of the varying chamber pressure and theexternal volume between the verifier and the DUT.
 5. The flow verifierof claim 2, wherein the critical flow time period t_(cf) is definedbetween a point in time when the downstream valve is shut, to a point intime when a ratio between P_(d) and P_(u) exceeds the critical pressureratio limit, α_(p0), as given by:${t_{c} = \frac{V( {a_{pc} - a_{p\; 0}} )}{C^{\prime}{{Af}_{g}( {M,\gamma,T} )}}},$where V_(c) is chamber volume, a_(p0) is initial pressure ratio betweenthe upstream and the downstream of the nozzle at t=0, C′ is dischargecoefficient for the nozzle, A is cross-sectional area of the nozzlethroat, f_(g)(M,γ, T)${f_{g}( {M,\gamma,T} )} = {( {\frac{RT}{M}\frac{2\gamma}{\gamma + 1}} )^{1/2}( \frac{2}{\gamma + 1} )^{1/{({\gamma - 1})}}}$where M is the molecular weight of the fluid, R is the universal gasconstant, T is the gas temperature, and γ is a ratio of specific heatsC_(p) and C_(v) of the fluid, C_(p) being the gas heat capacity atconstant pressure, and C_(v) being the gas heat capacity at constantvolume.
 6. The flow verifier of claim 1, wherein flow rate of the fluidduring the critical flow period t_(cf) is given by:${Q = {C^{\prime}{{AP}_{\mu}( {\frac{RT}{M}\frac{2\gamma}{\gamma + 1}} )}^{1/2}( \frac{2}{\gamma + 1} )^{1/{({\gamma - 1})}}}},$where T is a temperature of the fluid; A is a cross-sectional area ofnozzle orifice, C′ is a discharge coefficient, M is a molecular weightof the fluid, R is a universal gas law constant, and P_(d), P_(u), and γare defined as in claim
 1. 7. The flow verifier of claim 3, wherein thecontroller is configured to verify the measurement of the fluid deliverydevice by: a) opening the upstream valve and the downstream valve; b)providing a flow set point for the device; c) waiting until pressurewithin the chamber reaches a steady state and stabilizes; d) start torecord the chamber gas pressure and the chamber gas temperature for flowcalculation; e) shut the downstream valve, so that the pressure withinthe chamber rises; f) wait for a period less than the critical flowperiod t_(cf) for flow verification; g) open the downstream valve withina critical time period as measured from when the downstream valve wasshut; and h) compute the flow rate of the fluid into the chamber using:$Q_{in} = {\frac{k_{0} \cdot T_{stp} \cdot V_{c}}{P_{stp}}\frac{\mathbb{d}\;}{\mathbb{d}t}( \frac{P}{T} )}$where V_(c) is the chamber volume, T_(stp) is about 273.15K, P_(stp) isabout 1.01325e5 P_(a), K₀ is about 6×10⁷ in SCCM units and 6×10⁴ in SLMunits P is the chamber pressure measured by the pressuresensor/transducter T is the gas temperature measured by the temperaturesensor.
 8. The flow verifier of claim 7 wherein the critical nozzleseparates the chamber volume of the ROR verifier from external plumbingto the DUT, so that the external volume information is irrelevant to theflow rate calculation of the ROR mass flow verifier, and no setupcalibration is needed to determine the external volume between the flowverifier and the DUT.
 9. The flow verifier of claim 8, wherein the flowverifier is operable in a continuous-pulse-semi-real time (CPSR)operation mode in which the controller causes the pressure andtemperature measurements to be made by the pressure sensor and thetemperature sensor during each of a plurality of verification timeperiods, each verification time period starting when the downstreamvalve is shut, and ending when the downstream valve is opened before thecritical flow period t_(cf) lapses from the time the downstream valvewas shut, such that the flow across the nozzle is always at the criticalflow condition and the varying chamber pressure has substantially noimpact on the flow rate and the downstream pressure of the DUT.
 10. Theflow verifier of claim 9, wherein the flow rate computed by thecontroller is an averaged flow rate for multiple runs in the CPSR mode,so that a variance in the computed flow rate caused by measurement noisein the pressure sensor and temperature sensor is minimized.
 11. The flowverifier of claim 1, wherein the critical flow nozzle is configured soas to restrict flow of the fluid through the nozzle to a critical flow.12. A method of verifying measurement of a flow delivery device,comprising: placing a critical flow nozzle along the flow path of thefluid between the mass flow verifier and the DUT to maintain flow of thefluid so that during a critical flow time period, flow of the fluidacross the nozzle and pressure of the fluid upstream of the nozzle ofthe remains substantially constant and substantially insensitive to therise of the pressure within the chamber; causing the fluid to flow fromthe device into a chamber along a flow path, while an inlet and anoutlet valve of the chamber is kept open; allowing a flow rate of thefluid into the chamber and a pressure of the fluid within the chamber toreach a steady state; closing a valve downstream of the chamber so thatpressure of the fluid begins to rise within the chamber; and makingmeasurements of fluid pressure and fluid temperature within the criticalflow time period to measure a rate of rise of pressure of the fluidwithin the chamber and using the measured rate of rise of pressure tocompute the flow rate of the fluid along with the measurements of fluidtemperature; wherein the critical flow nozzle is configured to restrictflow of the fluid across the nozzle so that a critical flow condition issatisfied during the critical flow time period, and wherein the criticalflow condition is given mathematically by:${{\frac{P_{d}}{P_{u}} \leq a_{pc}} = ( \frac{2}{\gamma + 1} )^{\frac{\gamma}{\gamma - 1}}},$where P_(d) is pressure of the fluid within the chamber and downstreamof the critical flow nozzle, P_(u) is pressure of the fluid upstream ofthe critical flow nozzle, γ is given by γ=C_(p)/C_(v) and is a ratio ofspecific heats C_(p) and C_(v) of the fluid, where C_(p) is heatcapacity of the fluid at constant pressure, and C_(v) is heat capacityof the fluid at constant volume, and α_(pc) is a critical flow parameterrepresenting maximum allowable ratio between P_(d) and P_(u) for whichflow of the fluid across the nozzle will remain substantially constantand substantially insensitive to any variation in pressure within thechamber.
 13. The method of claim 12, wherein the flow rate of the fluidis computed using:$Q_{in} = {\frac{k_{0} \cdot T_{stp} \cdot V_{c}}{P_{stp}}\frac{\mathbb{d}\;}{\mathbb{d}t}( \frac{P}{T} )}$where P and T are measured by the pressure sensor and the temperaturesensor during the verification period which is within the critical flowperiod such that the varying chamber pressure has not impact on thedownstream pressure of the DUT.
 14. The method of claim 13, wherein thepressure and temperature measurements are made during each of aplurality of verification time periods, each verification time periodstarting when the downstream valve is shut, and ending when thedownstream valve is opened before the critical flow time period t_(cf)lapses from the time the downstream valve was shut; and wherein thecomputed flow rate is an averaged flow rate during multiple runs in theCPSR mode so that measured noise is minimized.